Compact electromagnetic plasma ignition device

ABSTRACT

A quarter wave coaxial cavity resonator for producing corona discharge plasma from is presented. The quarter wave coaxial cavity resonator has a folded cavity made of opposing concentric cavity members that are nested together to form a continuous cavity ending in a aperture. A center conductor with a tip is positioned in the cavity. The folded cavity advantageously permits the coaxial cavity resonator to resonate at a lower operating frequency than an unfolded quarter wave coaxial cavity resonator of the same length. Embodiments of the quarter wave coaxial cavity resonator use narrower apertures to reduce radiative losses, and include center conductors that are reactive load elements, such as helical coils. When a radio frequency (RF) oscillation is produced in the quarter wave coaxial cavity resonator, corona discharge plasma is formed at the tip of the center conductor. The corona discharge plasma can be used to ignite combustible materials in combustion chambers of combustion engines.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is continuation application that claims priority to andthe full benefit of U.S. Non-Provisional patent application Ser. No.14/272,560, entitled “COMPACT ELECTROMAGNETIC PLASMA IGNITION DEVICE,”filed May 8, 2014, which claims priority to and is a divisionalapplication of U.S. Non-Provisional patent application Ser. No.12/756,920, entitled “COMPACT ELECTROMAGNETIC PLASMA IGNITION DEVICE,”filed Apr. 8, 2010, which claims priority to a continuation-in-partapplication of U.S. Non-Provisional patent application Ser. No.12/023,770, entitled “PLASMA GENERATING IGNITION SYSTEM AND ASSOCIATEDMETHOD,” filed on Jan. 31, 2008.

TECHNICAL FIELD

Embodiments of the present disclosure relate generally to systems,devices, and methods for using a quarter wave coaxial cavity resonatoras an ignition source for a combustion engine.

BACKGROUND OF THE INVENTION

There are two basic methods used to ignite combustion mixtures. Autoignition through compression and spark ignition. Today a very largenumber of spark ignited (SI) engines are in use, consuming a limitedfossil fuel supply. A significant environmental and economic benefit isobtained by making combustion engines more efficient. Higher thermalefficiencies for SI engines are obtained through operation with leanerfuel air mixtures and through operations at higher power densities andpressures. Unfortunately, as mixtures are leaned, they become moredifficult to ignite and combust. More energetic sparks with largersurfaces are required for reliable operation, for example using multiplespark plugs per cylinder systems or rail-plug igniters. As moreenergetic sparks are used, their overall ignition efficiency is reducedbecause the higher energy levels are detrimental to the spark pluglifetime. These higher energy levels also contribute to the formation ofundesirable pollutants. Therefore it would be desirable to have a sparkplug capable of igniting leaner fuel air mixtures than traditional sparkignition sources.

Plasma ignition sources provide an alternative to traditional sparkignition and opens the door to more efficient, leaner and cleanercombustion resulting in associated economic and environmental benefits.Prior art methods and apparatuses describe using plasma as an ignitionmeans for combustion engines. One method of generating plasma involvesusing a radio frequency (RF) source and a quarter wave coaxial cavityresonator to generate corona discharge plasma. The prior art uses aradio frequency (RF) oscillator and amplifier to generate the requiredRF power at a desired frequency. RF oscillators and amplifiers can beeither semiconductor or electron tube based, and are well known in theart. The RF oscillator and amplifier are coupled to the quarter wavecoaxial cavity resonator, which in turn develops a standing RF wave inthe cavity at the frequency determined by the RF oscillator. Byelectrically shorting the input end of the quarter wave coaxial cavityresonator and leaving the other end electrically open, the RF energy isresonantly stepped-up in the cavity to produce a corona discharge plasmaat the open end of the quarter wave coaxial cavity resonator. The coronadischarge plasma can function generally as an ignition means forcombustible materials and specifically in a combustion chamber of acombustion engine.

A quarter wave coaxial cavity resonator is designed to have anelectrical length that is approximately one-quarter of the radiofrequency delivered from the RF oscillator and amplifier, althoughcavities that are multiples of one-quarter of the radio frequency willalso work. The electrical length of the quarter wave coaxial cavityresonator depends upon the physical geometry of the cavity, thetemperature, pressure and environment at the open end of the cavity, aswell was whether one or more dielectrics are used to plug or seal theend of the cavity.

Energy consumption is minimized and the corona discharge is maximizedwhen the quarter wave coaxial cavity resonator and radio frequency areappropriately matched. However, the cavity still generates a coronadischarge plasma for a range of frequencies around the optimal frequencyas well as at higher harmonics of the optimal frequency. An unmatchedquarter wave coaxial cavity resonator generally results in lowerefficiencies and less power being delivered to the quarter wave coaxialcavity resonator and therefore potentially less corona discharge plasma.When the corona discharge plasma is used as an ignition source for acombustion chamber, a reduction in the amount or strength of the coronadischarge plasma is undesirable as it could result in non-ignition ofcombustible materials in the combustion chamber. Therefore, it is bestto closely match the generated radio frequency to the quarter wavecoaxial cavity resonator to maximize energy efficiency and maximizecorona discharge plasma generation.

However, in practice, the resonant frequency of a quarter wave coaxialcavity resonator may not be optimally matched with the RF oscillator andamplifier. This can occur for any number of reasons, including improperselection of frequency in the RF oscillator, mechanical fatigue andwearing of the quarter wave coaxial cavity resonator or dielectric, oreven transient changes in the resonant frequency of the quarter wavecoaxial cavity resonator due to, for example, the formation of thecorona discharge plasma itself or other changes in the environment nearthe region of the cavity. Therefore, it is desired that the RFoscillation be dynamically generated and modulated in such a way that itis closer to the resonant frequency of the quarter wave coaxial cavityresonator in order to attain the optimal frequency for corona dischargeplasma generation.

Also, the prior art systems and apparatuses that describe systems,devices, and methods for using plasma as an ignition means in acombustion engine generally require redesign of electronic ignitioncontrol systems, the fuel injection systems, or even the combustionchambers of the engines themselves to function. Therefore, there existsa need for a corona discharge plasma ignition device that can functionas a replacement for a spark plug in an internal combustion enginewithout requiring substantial modification to the engine, ignitioncontrol system or associated connections and circuitry.

Further, to use a plasma ignition device in place of a spark plug mayrequire that the device be approximately the same size and geometry asan existing spark plug. Because most spark plugs are small, just severalcentimeters, the plasma ignition device must use very high frequenciesto develop standing waves in a similarly sized package. Higherfrequencies generally require more expensive power supplies andconduction losses generally increase as frequencies increase. Lossesrequire more robust power supplies, further increasing expenses and makethe plasma ignition device more prone to failures due to insufficientpower. Therefore there exists a need for a plasma ignition device thatuses energy more efficiently or uses lower frequencies.

SUMMARY OF THE INVENTION

The present disclosure meets the above and other needs. A quarter wavecoaxial cavity resonator (QWCCR) is adapted to operate in the nextgeneration of lean high efficiency internal combustion engines. Inembodiments, the QWCCR comprises a folded cavity that permits the use oflower operating frequencies than an unfolded cavity of comparablelength. In embodiments, the QWCCR comprises a reduced aperture geometrythat reduces the amount of aperture radiation that is lost through theopen end. In embodiments, the QWCCR comprises a reactive load centerconductor to decrease the necessary operating frequency for a givencavity length and boost the amount of stored energy in the QWCCR. Inembodiments, the QWCCR is adapted to mate with the combustion chamber ofa combustion engine.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying figures depict multiple embodiments of the compactelectromagnetic plasma ignition device. A brief description of eachfigure is provided below. Elements with the same reference numbers ineach figure indicate identical or functionally similar elements.

Additionally, as a convenience, the left-most digit(s) of a referencenumber identifies the drawings in which the reference number firstappears.

FIG. 1 is a schematic diagram of a prior art ignition system using aspark plug as an ignition source.

FIG. 2 is a schematic diagram of a prior art ignition system using acoaxial cavity resonator as an ignition source.

FIG. 3 is a schematic diagram of an embodiment of the invention wherethe coaxial cavity resonator is used as a frequency determining element.

FIG. 4 is a schematic diagram of an alternative embodiment of theinvention where the coaxial cavity resonator is used as a frequencydetermining element and where a power supply delivers additional powerto the power shaping means.

FIG. 5 is a cross-sectional view of one embodiment of the coaxial cavityresonator where the power shaping means comprises a negative resistancedevice that is integrated into the center conductor of the coaxialcavity resonator.

FIG. 6 is a cross-sectional view of an alternate embodiment of thecoaxial cavity resonator where the power shaping means comprises a sparkgap that is integrated into the center conductor of the coaxial cavityresonator.

FIG. 7 is a cross-sectional view of an alternate embodiment of thecoaxial cavity resonator where the power shaping means comprises a sparkgap that is near the top of the center conductor of the coaxial cavityresonator.

FIG. 8 is a cross-sectional view of an alternate embodiment of thecoaxial cavity resonator where the power shaping means comprises a sparkgap near the base of the center conductor of the coaxial cavityresonator.

FIG. 9 is a cross-sectional view of an alternate embodiment of thecoaxial cavity resonator with a simple probe providing an electricalfeedback sense.

FIG. 10 is a cross-sectional view of an alternate embodiment of thecoaxial cavity resonator with a loop pickup providing an electricalfeedback sense.

FIG. 11 is a cross-sectional view of an alternate embodiment of thecoaxial cavity resonator with separate waveguides providing power and anelectrical feedback sense.

FIG. 12 is a cross-sectional view of an alternate embodiment of thecoaxial cavity resonator with a common waveguide providing power and anelectrical feedback sense.

FIG. 13 is a cross-sectional view of an alternate embodiment of thecoaxial cavity resonator with a power connection entering through thebase of the cavity and an electrical feedback sense.

FIGS. 14a, 14b and 14c are cutaway views of embodiments of the coaxialcavity resonator having an empty cavity, a filled or partially filledcavity, and a sealed cavity.

FIG. 15 illustrates a view of an exemplary QWCCR coaxial structure.

FIG. 16 illustrates a contour plot of the ratio of internal to externalstored energy.

FIG. 17 illustrates a contour plot of Qrad.

FIG. 18 illustrates a contour plot of the Q/2 for brass at 2.45 GHzusing an air dielectric.

FIG. 19 illustrates a contour plot of Ea in (kV cm-1 W-½) for brass at2.45 GHz using an air dielectric.

FIG. 20 illustrates a view of an exemplary QWCCR design andimplementation.

FIGS. 21a, 21b, 21c, and 21d illustrates views of exemplary QWCCRshaving reduced aperture geometries.

FIGS. 22a and 22b illustrate 2D and 3D views of an exemplary taperedQWCCR having threads for mounting in a combustion engine.

FIGS. 23a and 23b illustrate 2D and 3D views of an exemplary foldedQWCCR having threads for mounting in a combustion engine.

FIG. 23c illustrates an unfolded QWCCR for purposes of explainingfeatures of a folded QWCCR.

FIGS. 24a and 24b illustrate views of high Q folded QWCCRs havingshortened geometries.

FIGS. 25a and 25b illustrate views of folded QWCCRs having helicalreactive loading.

DETAILED DESCRIPTION

FIG. 1 and FIG. 2 detail the prior art ignition systems. Exemplaryembodiments of the present invention are detailed in FIGS. 3-25.

Prior Art Ignition System with a Spark Plug

Referring now to the schematic diagram of a prior art ignition system100 depicted in FIG. 1, a battery 102 connects to an electronic ignitioncontrol system 104 which is connected by a spark plug wire to theterminal end of a spark plug 106.

In a typical prior art ignition system 100, like that found in anautomobile, a battery 102 provides electrical power to an electronicignition control system 104. The electronic ignition control system 104determines the proper timing for triggering an ignition event, and atthe appropriate time sends a high voltage pulse via a spark plug wire tothe terminal end of a spark plug 106. The high voltage pulse causes aspark to discharge at the tip of the spark plug 106 that is displacedinside of a combustion chamber (not shown). The spark ignitescombustible material, such as gasoline vapor, that is inside thecombustion chamber of a combustion engine, completing the ignitionsequence.

Prior Art Ignition System with a Stand-Alone Coaxial Cavity Resonator

Referring now to the schematic diagram of a prior art coaxial cavityresonator ignition system 200 depicted in FIG. 2, a power supply 202connects to a radio frequency (RF) oscillator 204 that is connectedthrough an electronic ignition control system 104 to an amplifier 206that is connected to a stand-alone coaxial cavity resonator 208. Anexemplary system using a stand-alone coaxial cavity resonator 208 isdescribed in U.S. Pat. No. 5,361,737 to Smith et al. herein incorporatedby reference. A coaxial cavity resonator may also be referred to as aquarter wave coaxial cavity resonator.

In the prior art coaxial cavity resonator ignition system 200, the powersupply 202 provides electrical power to an RF oscillator 204. The RFoscillator 204 generates an RF signal at a frequency chosen toapproximate the resonant frequency of the stand-alone coaxial cavityresonator 208. The RF oscillator 204 delivers the RF signal to anelectronic ignition control system 104 that determines the proper timingfor triggering an ignition event, and at the appropriate time forwardsthe RF signal to the amplifier 206 for amplification. The amplifier 206amplifies the RF signal to the proper power to create sufficientlyenergetic corona discharge plasma 210 at the discharge tip of thestand-alone coaxial cavity resonator 208 to ignite a combustiblematerial in the combustion chamber of a combustion engine.

Self-Oscillating Coaxial Cavity Resonator Ignition System

Referring now to an embodiment of the present disclosure depicted inFIG. 3, a battery 102 connects to an electronic ignition control system104 which is connected to a power shaping means 302. The power shapingmeans 302 is operably connected to a coaxial cavity resonator 304 suchthat the power shaping means 302 and the coaxial cavity resonator 304are in a feedback loop with one another to form a self-oscillatingcoaxial cavity resonator ignition system 300.

In the embodiment of FIG. 3, the battery 102 is a standard battery suchas that found in an automobile or any other convenient power source aswould be understood in the art, including but not limited to analternator, a generator, a solar cell, or fuel cell. The battery 102powers the electronic ignition control system 104. The electronicignition control system 104 outputs an impulse, e.g., a high voltagepulse, at the appropriate time to trigger ignition. The power shapingmeans 302 accepts the impulse, e.g., the high voltage pulse through aspark plug wire, from the electronic ignition control system 104.Parasitically using only the power supplied in the impulse from theelectronic ignition control system 104, the power shaping means 302regulates, amplifies, or generates the necessary electrical voltage,amplitude, and time-varying characteristics of the electrical waveformoutput to the coaxial cavity resonator 304. Because the power shapingmeans 302 varies the electrical waveform in a “time-varying” manner, thepower shaping means 302 is also called an energy shaping means; energybeing the rate at which power is expended. Thus power shaping means 302and energy shaping means may be used interchangeably in this disclosure.The term waveform in the various embodiments disclosed herein is meantto encompass any suitable electrical or electromagnetic power whose timevarying characteristics help create the RF oscillations as would beunderstood by one of ordinary skill in the art, including but notlimited to, one or more high-voltage DC electrical pulses, an amplifiedAC signal, or RF energy delivered by waveguide.

Together, the power shaping means 302 and the coaxial cavity resonator304 form a self-oscillating coaxial cavity resonator ignition system 300and develop a sustained RF oscillation, or time limited RF oscillationsuch as an RF pulse, that is close to or at the resonant frequency ofthe coaxial cavity resonator 304 which results in optimal coronadischarge plasma 210 generation. In one embodiment, the duration of thesustained RF oscillation is a short period ignition pulse as would beused for internal combustion engines such as those used in automobiles.In another embodiment, the duration of the sustained RF oscillation isapproximately continuous, generating corona discharge plasma 210 duringthe period of engine operation, as in the case of a jet engine.

The power shaping means 302 is any electrical circuitry capable ofcreating an RF oscillation in conjunction with the coaxial cavityresonator 304, without requiring a separate RF oscillator, to generatecorona discharge plasma 210. In different embodiments, the power shapingmeans 302 comprises various combinations of electron tubes or electrondrift tubes, examples of which are traveling wave tubes or Magnetrons,Amplitrons, semiconductors including negative resistance devices,inductive or capacitive elements, or spark gaps. As is known in the art,various devices and circuit designs are capable of triggering,amplifying, and maintaining RF oscillations indefinitely or for alimited time period. By using the coaxial cavity resonator 304 as partof a frequency determining circuitry, the frequency of the oscillationis made to more closely approximate the resonant frequency of thecoaxial cavity resonator 304.

In an exemplary embodiment, the RF oscillations are between about 750MHz and 7.5 GHz. A coaxial cavity resonator 304 measuring between 1 to10 cm long approximately corresponds to an operating frequency in therange of 750 Mhz to 7.5 Ghz. The advantage of generating frequencies inthis range is that it allows the geometry of a body containing thecoaxial cavity resonator 304 to be dimensioned approximately the size ofthe prior art spark plug 106.

In one embodiment of the self-oscillating coaxial cavity resonatorignition system 300 in FIG. 3, and in other embodiments described laterin FIGS. 4-13, the power shaping means 302 and the coaxial cavityresonator 304 are contained in a body dimensioned approximately the sizeof the prior art spark plug 106 and adapted to mate with the combustionchamber of a combustion engine (not shown). In another embodiment, thebody is a modified prior art spark plug 106 body comprised of steel orother metals. A connection terminal (not shown) on the bodyapproximating that of the prior art spark plug 106 accepts a spark plugwire from the ignition control system 104. In the embodiment of theinvention of FIG. 3, the system 300 is powered solely by the impulsedelivered from the ignition control system 104 and therefore can be usedas a replacement spark plug 106 without requiring substantialmodifications to the engine, ignition system, or associated connectionsand circuitry. In another embodiment, the coaxial cavity resonator 304is contained in the body adapted for mating with the combustion chamberand the power shaping means 302 resides outside the body.

Powered Self-Oscillating Coaxial Cavity Resonator Ignition System

Referring now to the embodiment depicted in FIG. 4, a power supply 202connects to both an electronic ignition control system 104 and the powershaping means 302. The electronic ignition control system 104 isconnected to a power shaping means 302. The power shaping means 302 isoperably connected to a coaxial cavity resonator 304 such that the powershaping means 302 and the coaxial cavity resonator 304 are in a feedbackloop with one another to form a powered self-oscillating coaxial cavityresonator ignition system 400.

FIG. 4 is similar to FIG. 3 but has a power supply 202 that replaces thebattery 102 of FIG. 3, and the power supply is electrically connected tothe power shaping means 302. Because the power supply 202 providesregulated power to the power shaping means 302, the power shaping means302 does not have to run parasitically solely from the impulse energydelivered from the electronic ignition control system 104 as in oneembodiment detailed in FIG. 3. In a powered self-oscillating coaxialcavity resonator ignition system 400, the regulated power may be used invarious embodiments to power negative resistance devices 502 (shown onFIG. 5) or electron tubes. As is generally known in the art, onecategory of semiconductor devices called negative resistance devices502, including Gunn diodes, IMPATT diodes, or TRAPATT diodes, can beused to turn direct current (DC) impulses into RF energy. Gunn diodesmay also be referred to as a type of transferred electron device (TED).A small offset voltage, or bias, puts the negative resistance device 502into the proper operating range for having the characteristic negativeresistance necessary for generating RF waveforms. When a negativeresistance device or electron tube is matched to a resonator, forexample a coaxial cavity resonator 304, and given an additional pulsedelectrical stimulus, the negative resistance device 502 or electron tubeand coaxial cavity resonator 304 together generate the desired RFwaveform, thus forming a powered self-oscillating coaxial cavityresonator ignition system 400.

In the embodiment of FIG. 4, feedback from the power shaping means 302and coaxial cavity resonator 304 is coupled back to the electronicignition control system 104 for on-board diagnostics as well as controlof other engine functions such as fuel flow, ignition advance, emissioncontrol and other systems as would be obvious to one having ordinaryskill in the art.

In an alternative embodiment of a powered self-oscillating coaxialcavity resonator ignition system 400, the regulated power powers an RFamplifier in the power shaping means 302 for generating more energeticcorona discharge plasma 210. For example, a suitable field effecttransistor (FET), HEMT, MMIC or other semiconductor amplifier capable ofoperating in the RF spectrum is used along with a simple probe 902 orpickup loop 1002 as a feedback mechanism in making an RF oscillator.More energetic corona discharge plasma 210 allows easier ignition of awider range of combustible materials. In yet another embodiment, theregulated power supports a power shaping means 302 with additionalcircuitry to allow the electronic ignition control system 104 to utilizelow voltage signals or even data transmissions to initiate an ignitionsequence, instead of the standard high voltage impulses used in mostignition systems today.

Coaxial Cavity Resonator with Negative Resistance Device

Referring now to the embodiment of the coaxial cavity resonator 304depicted in FIG. 5, a power feed wire 512 enters the coaxial cavityresonator 304 through an insulated guide 510, and attaches to thesuspended center conductor 504. The insulated guide 510 prevents contactbetween the power feed wire 512 and the coaxial cavity resonator 304.The insulated guide 510 terminates at the wall of the coaxial cavityresonator 304 near the base 516. In alternate embodiments, the insulatedguide 510 extends into the coaxial cavity resonator 304. In alternateembodiments, the power feed wire 512 enters into the coaxial cavityresonator 304 through the base 516. In an alternate embodiment, thepower feed wire 512 extends into the coaxial cavity resonator 304without an insulated guide 510.

The suspended center conductor 504 is suspended above the base 516 ofthe coaxial cavity resonator 304 by physical contact with a negativeresistance device 502, by filling the internal cavity of the coaxialcavity resonator 304 with a supporting dielectric (not shown), or by anyother supporting means as known in the art. At one end, the proximalend, the suspended center conductor 504 is electrically connected to thenegative resistance device 502 near the base 516. At the other end, thedistal end, the suspended center conductor 504 has a discharge electrode506 where the corona discharge plasma 210 is generated. The negativeresistance device 502 is electrically connected to the base 516 of thecoaxial cavity resonator 304. An electrical return path 514 attachesdirectly to the coaxial cavity resonator 304. In an alternativeembodiment, the negative resistance device 502 is physically raised fromthe base 516 of the coaxial cavity resonator 304 on a bottom stub of thecenter conductor 504. In alternate embodiments, the negative resistancedevice 504 is positioned anywhere along length of the center conductor504 between the base 516 and the discharge electrode 506. In alternateembodiments, the negative resistance device 502 is electricallyconnected to the wall of the coaxial cavity resonator 304 instead of thebase 516. In an alternate embodiment, the negative resistance device 502is electrically connected to the electrical return path 514.

The power feed wire 512 delivers both a small direct current (DC) biasand an electrical impulse to the suspended center conductor 504. Thepower feed wire 512 is insulated from the rest of the coaxial cavityresonator 304 by the insulated guide 510. The DC bias delivered by thepower feed wire 512 is conducted through the suspended center conductor504 to the negative resistance device 502. The DC bias puts the negativeresistance device 502 in the proper operating range for having thecharacteristic negative resistance necessary for generating RFwaveforms. The electrical return path 514 completes the DC electricalcircuit, allowing proper DC biasing of the negative resistance device502. The electrical impulse, also delivered on the power feed wire 512,then starts the RF oscillation between the negative resistance device502 and coaxial cavity resonator 304. The RF oscillation creates astanding wave in the coaxial cavity resonator 304, resulting in coronadischarge plasma 210 being generated at the discharge electrode 506. Thedischarge electrode 506 is formed from or coated with a metal orsemi-metallic conductor, for example stainless steel, that can withstandthe temperature conditions near the corona discharge plasma 210 withoutdeformation, oxidation, or loss.

Coaxial Cavity Resonator with Spark Gap

Referring now to the embodiment of the coaxial cavity resonator 304depicted in FIG. 6, a power feed wire 512 enters the coaxial cavityresonator 304 through an extended insulated guide 610, and attaches tothe suspended center conductor 504. The extended insulated guide 610prevents contact between the power feed wire 512 and the coaxial cavityresonator 304 The suspended center conductor 504 is suspended above thebase 516 of the coaxial cavity resonator 304 by physical contact withthe extended insulated guide 610. In alternative embodiments, thesuspended center conductor 504 is suspended by filling the internalcavity of the coaxial cavity resonator 304 with a supporting dielectric(not shown), or by any other supporting means as known in the art. Inalternate embodiments, the extended insulated guide 610 is an insulatedguide 510 and does not extend into the coaxial cavity resonator 304. Inalternate embodiments, the extended insulated guide 610 contacts thesuspended center conductor 504 anywhere along the length of thesuspended center conductor 504 up to the discharge tip 506. In alternateembodiments, the power feed wire 512 enters into the coaxial cavityresonator 304 through the base 516.

At one end, the proximal end, the suspended center conductor 504 has anelectrically open spark gap 602 near the base 516. At the other end, thedistal end, the suspended center conductor 504 has a discharge electrode506 where the corona discharge plasma 210 is generated. On the base 516side of the spark gap 602 is a slightly raised bottom stub centerconductor 604. An electrical return path 514 also attaches to thecoaxial cavity resonator 304. In an alternate embodiment, the spark gap602 is positioned anywhere along the length of the center conductor 504between the base 516 and the discharge electrode 506. In an alternativeembodiment, the spark gap 602 is between the suspended center conductor504 and the base 516.

The power feed wire 512 delivers an electrical impulse to the suspendedcenter conductor 504. The power feed wire 512 is insulated from the restof the coaxial cavity resonator 304 by the extended insulated guide 610that extends into the cavity of the coaxial cavity resonator 304. Theelectrical impulses necessary for the generation of RF waveforms requireshort pulses with sharp rise-times, and the center conductor 504 and thestub center conductor 604 on either side of the spark gap 602 areconstructed to withstand the possible erosion due to these sparks. Theelectrical impulses trigger sparks to arc across the spark gap 602,ringing the coaxial cavity resonator 304 and triggering RF oscillationswhich then form standing waves in the coaxial cavity resonator 304. Theresonating standing waves in the coaxial cavity resonator 304 result incorona discharge plasma 210 being generated at the discharge electrode506.

Referring now to the embodiments of the coaxial cavity resonator 304depicted in FIGS. 7 and 8, a spark wire 712 enters the coaxial cavityresonator 304 through an insulated guide 510, and creates anelectrically open wire spark gap 702 with the center conductor 704. Thecenter conductor 704 is attached to the base 516 of the coaxial cavityresonator 304. The center conductor 704 has a discharge electrode 506 atthe distal end of the coaxial cavity resonator 304. An electrical returnpath 514 also attaches to the coaxial cavity resonator 304.

FIGS. 7 and 8 differ only in the location of the spark wire 712 andinsulated guide 510, and function similarly to embodiment depicted inFIG. 6. The spark wire 712 allows an electrical impulse to arc acrossthe wire spark gap 702 to the center conductor 704. The spark wire 712is insulated from the rest of the coaxial cavity resonator 304 by theinsulated guide 510 that also may extend into the cavity of the coaxialcavity resonator 304 similar to the extended insulated guide 610 of FIG.6 (not shown).

In alternate embodiments, the internal cavity 1404 of the coaxial cavityresonator 304 is filled with a dielectric (shown in FIG. 14b and FIG.14c ) that does not prevent a spark from bridging the spark gap 602 orwire spark gap 702. In an alternate embodiment, the spark gap 602 isbetween the suspended center conductor 504 and the wall of the coaxialcavity resonator 304. In an alternate embodiment, the wire spark gap 702is between the suspended center conductor 504 and the electrical returnpath 514. Various other locations and arrangements for the spark gap 602and wire spark gap 702 are possible and would be obvious to one havingskill in the art. The above figures and descriptions represent merelyexemplary embodiments of the invention.

Coaxial Cavity Resonator with Feedback Sense

Referring now to the embodiments of the coaxial cavity resonator 304depicted in FIGS. 9 and 10, a power feed wire 512 enters the coaxialcavity resonator 304 through an extended insulated guide 610, andattaches to the center conductor 704. The center conductor 704 isattached to the base 516 of the coaxial cavity resonator 304 and theinternal cavity of the coaxial cavity resonator 304 may be filled with adielectric (not shown). The center conductor 704 has a dischargeelectrode 506 at the open end of the coaxial cavity resonator 304. Anelectrical return path 514 also attaches to the coaxial cavity resonator304. FIG. 9 depicts a simple probe 912 with an insulated probe guide 910that extends into the coaxial cavity resonator 304 and has an open endedprobe tip 902 that extends through the insulated probe guide 910 furtherinto the coaxial cavity resonator 304. FIG. 10 depicts a pickup loop1012 with an insulated loop guide 1010 that allows a wire loop 1002 toextend into the coaxial cavity resonator 304 and attach to an innersurface of the coaxial cavity resonator 304. In an alternate embodiment,a probe 902 is used as a power feed instead of the directly connectedpower feed wire 512. In an alternate embodiment, a wire loop 1002 isused as a power feed instead of the directly connected power feed wire512.

Referring now to the embodiment of the coaxial cavity resonator 304depicted in FIG. 11, an input waveguide 1102 is coupled to the coaxialcavity resonator 304. The input waveguide 1102 couples an electron tubedevice such as a magnetron, amplitron, traveling wave tube, or other RFamplifier to the coaxial cavity resonator 304. A feedback waveguide 1104provides feedback to the magnetron, traveling wave tube, or other RFamplifier. Referring now to the embodiment of the coaxial cavityresonator 304 depicted in FIG. 12, a waveguide 1202 is coupled to thecoaxial cavity resonator 304, similar to FIG. 11, but utilizing thewaveguide 1202 for both transferring power to the coaxial cavityresonator 304 and providing a feedback signal.

Referring now to the embodiment of the coaxial cavity resonator 304depicted in FIG. 13, a simple probe 912 with an open ended probe tip 902extends through the insulated probe guide 910 into the base 516 of thecoaxial cavity resonator 304 as a feedback sense. An RF cable 1302connects to the base 516 of the coaxial cavity resonator 304 and the RFcable center wire 1304 is electrically connected to the center conductor704. One or more loops 1308 used to energize the coaxial cavityresonator 304 are displaced further along the center conductor 704, andloop back to the RF cable shield 1306 and the base 516 of the coaxialcavity resonator 304. In alternate embodiments, the simple probe 912 andRF cable 1302 are placed at any convenient location on the coaxialcavity resonator 304 as would be understood by one of ordinary skill inthe art. In alternate embodiments, various combinations of simple probes912, pickup loops 1012, waveguides 1202, and feedback waveguides 1104and direct electrical coupling are used to energize the coaxial cavityresonator 304, provide a feedback sense, or both, as would be understoodby one of ordinary skill in the art.

A direct electrical coupling, a simple probe 912, a pickup loop 1012, awaveguide 1202, or a feedback waveguide 1104 provide a feedback senseback to the power shaping means 302 (not shown) for sensing theelectrical oscillations in the coaxial cavity resonator 304. The powershaping means 302 uses this electrical feedback as input to frequencydetermining circuitry resulting in the frequency of the oscillationsmore closely approximating the resonant frequency of the coaxial cavityresonator 304. Direct electrical couplings, simple probes 912, pickuploops 1012, waveguides 1202, and feedback waveguides 1104 are well knownin the art for use with RF cavity resonators, as are other suitablefeedback devices that would be obvious to one having ordinary skill inthe art.

Coaxial Cavity Resonator

Referring now to FIGS. 14a, 14b, and 14c , in alternate embodiments thecenter conductor 704 and cavity wall 1402 of the coaxial cavityresonator 304 are each comprised of a material taken from the group ofcopper, brass, steel, platinum, silver, aluminum, or other goodelectrical conductors in order to provide high conductivity and lowpower absorption in the coaxial cavity resonator 304. Referring to FIG.14a , in one embodiment of the coaxial cavity resonator 304 the cavitywall 1402 defines a cavity 1404 having a hollow interior region.Referring to FIG. 14b , in another embodiment, the cavity 1404 of thecoaxial cavity resonator 304 is filled or partially filled with one ormore solid materials 1406 including, but not limited to, low electricalloss and non-porous ceramic dielectric materials, such as ones selectedfrom the group consisting of: aluminum oxide, silicon oxide, glass-mica,magnesium oxide, calcium oxide, barium oxide, magnesium silicate,alumina silicate, and boron nitride, to create a solid plug in thecavity. The solid materials 1406 form a plug in the coaxial cavityresonator 304 thereby minimizing physical perturbation of the combustionchamber and also minimizing electrical perturbation of the coaxialcavity resonator 304 by materials from the combustion chamber. Referringto FIG. 14c , in another embodiment, the cavity 1404 of the coaxialcavity resonator 304 is filled with other suitable dielectric materials1408 as would be known in the art including, but not limited to, arelatively unreactive gas such as nitrogen or argon. The cavity 1404 isthen sealed, for example, with one of the aforementioned solid materials1406, to prevent interaction with the combustion chamber.

Referring now to FIG. 15, a Quarter Wave Coaxial Cavity Resonator, orQWCCR 1500 is shown. The QWCCR 1500 has an outer conductor 1502 havingan interior wall 1508 with a radius of dimension b and an exterior wall1510, a base conductor 1504, and a center conductor 1506 having a radiusof a and a diameter of 2 a. The center conductor 1506 is also called acenter electrode. The center conductor 1506 has a tip 1516. The spacebetween the interior wall 1508 and the center conductor 1506 define acavity 1512. The QWCCR 1500 has an opening 1514, or aperture, at the endopposite the base conductor 1504. The center conductor 1506 ispositioned or disposed within the cavity 1512 and extends from the baseconductor 1504 towards the opening 1514. In embodiments, the centerconductor 1506 is entirely within the cavity 1512 and does not extendbeyond the opening 1514. In embodiments, the center conductor 1506 orthe tip 1516 are at, or extend beyond, the opening 1514. In embodiments,the center conductor 1506 is positioned equidistant from the interiorwall 1508 such that the center conductor 1506 extends through the centerof the QWCCR 1500. In embodiments, the center conductor 1506 iselectrically, electromagnetically, or physically connected to the baseconductor 1504.

Plasmas

Plasmas are categorized by their temperature and electron density.Microwave generated plasmas generally are more energetic (5-15 eVelectron temperature) than DC (1-2 eV electron temperatures).Unmagnetized, atmospheric pressure microwave plasmas provide higherionization and dissociation than DC due to their higher electron kineticenergy. Note that plasmas generated at atmospheric and higher pressuresare considered high pressure microwave plasmas and are distinct fromvacuum chamber plasmas.

The QWCCR 1500 creates microwave plasma by inducing electrical breakdownof a gas mixture surrounding the tip 1516 of the center conductor 1506using a microwave electric field. The QWCCR 1500 consists of a quarterwavelength resonant coaxial cavity into which electromagnetic energy iscoupled resulting in a standing electromagnetic field. This large fieldinduces a break-down in the gaseous medium surrounding the centerelectrode, or center conductor 1506, creating a plasma discharge at thetip 1516 of the center conductor 1506 as an ignition source.

Microwave and RF Gas Breakdown

The microwave electric field strength required to induce this breakdownis one ignition parameter. Gas electron dynamics govern the behavior ofsuch microwave breakdowns. Other factors include the initial freeelectron population, electron diffusion, drift, electron attachment andrecombination. The initial electron population, created by cosmic rays,photo ionization, radioactivity or other mechanisms, seeds theexponential increase in electrons during the breakdown process. Thisinitial electron population is usually unknown, but the nature of theexponential breakdown is not very different for wide ranges of initialelectron population densities.

During ionization, collisions of sufficiently energetic electrons withneutral particles or ions create additional electrons. The creation ofelectrons is balanced by various electron loss mechanisms. Diffusion isa minor loss mechanism due to its pressure dependence. At highpressures, electrons encounter many obstacles in their path, whichinhibit their ability to diffuse, so attachment and recombination areoften considered the dominant loss mechanism at pressures where plasmasare mainly collisional. Recombination becomes particularly relevant whensignificant concentration of ions and electrons are present, such as inalready established discharges, and the influence on the initialbreakdown parameters is diminished.

The electron energy absorption from an alternating electric field isquantified by defining an effective electric field, E_(eff), that isapproximately frequency independent. The compensation removes the phaselag effects of the applied frequency, ω, from the rms field, E_(rms),according to

$\begin{matrix}{E_{eff}^{2} = {E_{rms}^{2}\frac{v_{c}^{2}}{\omega^{2} + v_{c}^{2}}}} & (1)\end{matrix}$where v_(c) is the effective momentum collision frequency of theelectrons and neutral particles. This effective field is used to relatewell known DC breakdown voltages for various gases to AC breakdownvalues for uniform fields. A good approximation for air is v_(c)≈5·10⁹p, where p is the pressure in torr. At atmospheric pressures of 760 torrand above, excitations below 3,000 GHz will fall in the collisiondominated plasma domain. This justifies an approximation to the rmsbreakdown threshold, E_(b), in V/cm of a uniform microwave field in thecollisional regime given by

$\begin{matrix}{E_{b} \simeq {{30 \cdot 297}\frac{p}{T}}} & (2)\end{matrix}$where T is the temperature in K.

Electromagnetic Analysis

In embodiments, the microwave and RF gas breakdown equations are used todesign a QWCCR 1500 to create an ignition plasma for various pressuresand temperatures. Design variables of the QWCCR 1500 include thedielectric losses, and the radiation and conduction losses in the endsof the QWCCR 1500 resonator. The standing quarter wave electromagneticfields inside the resonator oscillate at a resonant frequency, w, storean energy, U, and dissipate a power, PL. In one embodiment, the QWCCR1500 coaxial geometry is shown in FIG. 15. The relationships between thegeometry and the material properties relate to the quality factor, theinput power and the maximum electromagnetic field developed.

Approximate Electromagnetic Field in the QWCCR

Neglecting fringing fields at the open end, the fields at the lowest ¼wave resonance in the cavity 1512 are transverse electromagnetic (TEM)fields as they exist inside coaxial cables. The quality factor, ameasure of the energy storage behavior, is the expression Q=β/(2α) of aresonant quarter wave transmission line section, where α+jβ is thecomplex valued electromagnetic propagation constant The fields fall offinversely with the radius, r, from the center. The direction of magneticfield is purely circumferential and the direction of the electric fieldis purely radial. The magnetic field intensity phasor, H, and theelectric field phasor, E, of the standing quarter wave inside theresonator can therefore be expressed as

$\begin{matrix}{{{H = {{H_{\varphi} \cdot {\hat{a}}_{\varphi}} = {\frac{I_{o}}{2 \cdot \pi \cdot r} \cdot {\cos\left( {\beta \cdot z} \right)} \cdot {\hat{a}}_{\varphi}}}},{and}}\mspace{11mu}} & (3) \\{E = {{E_{r} \cdot {\hat{a}}_{r}} = {\frac{V_{0}}{2 \cdot \pi \cdot r} \cdot {\sin\left( {\beta \cdot z} \right)} \cdot {{\hat{a}}_{r}.}}}} & (4)\end{matrix}$I₀ is the peak current at the base conductor 1504 of the cavity, V_(o)is the magnitude of peak potential, r is the radial distance from thecenter, z is the axial distance from the base conductor 1504 takenpositive toward the open end of the cavity 1512 and β=2π/λ is thewavenumber.

The Quality Factor, Relation to Tip Electric Field, and Energy Storage.

By definition,

$\begin{matrix}{{Q = \frac{\omega \cdot U}{P_{L}}},} & (5)\end{matrix}$where ω is the angular frequency, U is the time average energy and P_(L)is the time average power lost. Note, that after an extremely briefinitial cavity 1512 ringup during which the fields build up, the powerdelivered equals the power lost. The square of V₀ is proportional to theenergy stored, so (5) provides a relation for the developed tip electricfield through

$\begin{matrix}{U = {\frac{Q \cdot P_{L}}{\omega} \propto {V_{0}^{2}.}}} & (6)\end{matrix}$

At resonance, the stored energy oscillates between the electric fieldand the magnetic field. The time average stored energy in the cavity1512 volume, U, is given by integrating the field volume energydensities resulting in

$\begin{matrix}{{U = {{U_{m} + U_{e}} = {\frac{1}{4}{\int_{vol}\left( {{u{H}^{2}} + {ɛ{E}^{2}}} \right)}}}},{or}} & (7) \\{{U = {{\frac{{\ln\left( \frac{b}{a} \right)} \cdot \lambda}{64 \cdot \pi}\left( {{\mu \cdot I_{0}^{2}} + {ɛ \cdot V_{0}^{2}}} \right)} = \frac{{\ln\left( \frac{b}{a} \right)} \cdot \lambda \cdot ɛ \cdot V_{0}^{2}}{32 \cdot \pi}}},} & (8)\end{matrix}$where μ is the magnetic permeability and s is the electric permittivity.Since energy storage at resonance in the electric and magnetic fields isequal, U=2U_(m)=2U_(e). The ratio of the electric and magnetic fieldamplitudes, I₀ and V₀, gives η=√{square root over (μ/∈)}, the intrinsicimpedance of the volume in the cavity 1512. Noting that λ·f=1/√{squareroot over (μ∈)}, substitution of equation (8) into equation (5) andsolving for V₀, the center conductor peak tip potential results in:

$\begin{matrix}{V_{0} = {\sqrt{\frac{32 \cdot \pi \cdot Q \cdot P_{L}}{{\omega \cdot ɛ}{\cdot {\ln\left( \frac{b}{a} \right)} \cdot \lambda}}} = {4{\sqrt{\frac{\eta \cdot Q \cdot P_{L}}{\ln\left( \frac{b}{a} \right)}}.}}}} & (9)\end{matrix}$

The corresponding peak value of the electric field at radius a on thesurface of the center conductor 1506, E_(a), as given by equation (4) isthen:

$\begin{matrix}{E_{a} = {\frac{V_{0}}{2 \cdot \pi \cdot a} = {\frac{2}{\pi \cdot a}{\sqrt{\frac{\eta \cdot Q \cdot P_{L}}{\ln\left( \frac{b}{a} \right)}}.}}}} & (10)\end{matrix}$

The root mean square of this electric field will have to exceed thebreakdown strength given by equation (2). It is clear from equation (10)that to increase the field strength and induce breakdown, a should bemade as small as is practical. A higher intrinsic impedance, η, (lower∈, higher μ), more input power, P_(L), and a higher Q also increase thefield strength, but only in the square root. Since Q is a function ofthe geometry, it will be examined in more detail. Towards this, thepower losses in the cavity need to be examined.

Internal Power Losses

The power loss is composed of ohmic losses on the conductor 1502, 1504,1506 surfaces, P_(σ) dielectric losses, P_(σe), in the cavity 1512volume, and radiation losses, P_(rad), from the end of the open cavity1512. The ohmic losses depend on the surface resistance, R=√{square rootover (ω·μ_(c)/2·σ_(c))}, of the conductors 1502, 1504, 1506 where μ_(c)and σ_(c) are the magnetic permeability and the conductivity of theconductor 1502, 1504, 1506. The center conductor, the outer conductor1502, and the base conductor 1504 power losses, P_(ctr), P_(out), P_(b),are computed by integrating the ohmic power density over the conductorsurfaces, as given by:

$\begin{matrix}{{P_{\sigma} = {\frac{1}{2}{\int_{A}{R_{s}{H_{//}}^{2}}}}},{or}} & (11) \\{{P_{\sigma} = {{P_{ctr} + P_{out} + P_{b}} = {\frac{R_{s} \cdot I_{0}^{2}}{4 \cdot \pi}\left\lbrack {\frac{\lambda}{8 \cdot a} + \frac{\lambda}{8 \cdot b} + {\ln\left( \frac{b}{a} \right)}} \right\rbrack}}},} & (12)\end{matrix}$where H_(//) is the magnetic field parallel to the surface.

Interaction of matter with the electromagnetic fields can be verycomplicated, anisotropic, and frequency and temperature dependent. Byassuming that a simple isotropic low loss dielectric fills the cavity1512, the material can be characterized by its dielectric permittivity,∈, and its effective loss tangent, tan(δ_(e)). The effective losstangent represents any conductivity and any alternating molecular dipolelosses and are used to calculate an effective dielectric conductivity,σ_(e)≈ω·∈·tan(δ_(e)). The power dissipated by an alternating field for asimple low loss dielectric material is expressed by the volume integral,

$\begin{matrix}{P_{\sigma_{e}} = {{\frac{1}{2}{\int_{vol}{\sigma_{e}{E}^{2}}}} = {\frac{\sigma_{e} \cdot \eta^{2} \cdot I_{0}^{2}}{4 \cdot \pi}{\left( \frac{{\ln\left( \frac{b}{a} \right)} \cdot \lambda}{8} \right).}}}} & (13)\end{matrix}$

Substitution of the power losses thus far into equation (5) andcombining, the an internal quality factor, Q_(int) of the cavity,without considering radiation can then be defined as

$\begin{matrix}{Q_{int} = {\left( {Q_{ctr}^{- 1} + Q_{out}^{- 1} + Q_{b}^{- 1} + Q_{\sigma_{e}}^{- 1}} \right)^{- 1} = {\left( {{\frac{R_{s}}{2 \cdot \pi \cdot \eta}\left\lbrack {\frac{\left( {\frac{b}{a} + 1} \right)}{\frac{b}{\lambda} \cdot {\ln\left( \frac{b}{a} \right)}} + 8} \right\rbrack} + {\tan\left( \delta_{e} \right)}} \right)^{- 1}.}}} & (14)\end{matrix}$

Maximizing Q_(int) with respect to the radius ratio, b/a, results in theratio of b/a=3.59. This is the same ratio as a half-wave cavity. Byexamining these components of Q, it becomes apparent that thecontribution, Q_(out) of the outer conductor 1502, is greater than thecontribution Q_(ctr) of the center conductor 1506 by a factor of b/agiven conductivities. This suggest the use of a higher conductivitymaterial for the small amount of metal comprising the center conductor1506 to increase Q_(int). It can also be shown that the base conductor1504 and dielectric Q's, Q_(b), Q_(σe), are unaffected by the geometry(terms b/a and b/λ).

Up to this point the geometry for a maximum Q, suggests a b/a=3.59 andb/λ to be as large as feasible, but still below where higher resonancemodes appear, around 2π(a+b)≈λ. Any dielectric should have a minimumloss tangent and a low dielectric constant, and conductor 1502, 1504,1506 surface resistances should be kept as small as feasible. However,the rather significant radiation losses, due to the open aperture end,or opening 1514, still need to be considered.

Radiation Losses and Fringe Field Storage

A simple way to treat the radiation losses is to consider the apertureas admittance. For a coaxial line radiating into open space thisadmittance is known in the art. For a<<λ and b<<λ, the real part, G_(r),and the imaginary part, B_(r) is approximated by

$\begin{matrix}{{G_{r} \cong \frac{4 \cdot \pi^{5} \cdot \left\lbrack {\left( \frac{\frac{b}{\lambda}}{\frac{b}{a}} \right)^{2} - \left( \frac{b}{\lambda} \right)^{2}} \right\rbrack^{2}}{3 \cdot \eta \cdot {\ln^{2}\left( \frac{b}{a} \right)}}},{and}} & (15) \\{{B_{r} \cong {\frac{16 \cdot \pi \cdot \left( {\frac{\frac{b}{\lambda}}{\frac{b}{a}} - \frac{b}{\lambda}} \right)}{\eta \cdot {\ln^{2}\left( \frac{b}{a} \right)}} \cdot \left\lbrack {{E\left( \frac{2\sqrt{\frac{b}{a}}}{1 + \frac{b}{a}} \right)} - 1} \right\rbrack}},} & (16) \\{{{where}\mspace{14mu}{E(x)}} = {\int_{0}^{\frac{\pi}{2}}{{\sqrt{1 - {x^{2} \cdot {\sin^{2}(\theta)}}} \cdot d}\;\theta}}} & \;\end{matrix}$is the complete elliptical integral of the second kind. The lineintegral of the electric field from the center conductor 1506 to theouter conductor 1502 will give this potential difference V_(ab), acrossthis shunt admittance as:

$\begin{matrix}{{V_{ab}\text{❘}_{{\beta \cdot z} = {\pi/4}}} = {{\int_{a\rightarrow b}E_{r}} = {\frac{V_{0} \cdot {\ln\left( \frac{b}{a} \right)}}{2 \cdot \pi}.}}} & (17)\end{matrix}$

The power going to radiation, P_(rad), and the energy stored, U_(rad),are then

$\begin{matrix}{{P_{rad} = {{\frac{1}{2}{G_{r} \cdot V_{ab}^{2}}} = \frac{V_{0}^{2} \cdot \pi^{3} \cdot \left( \frac{b}{\lambda} \right)^{4} \cdot \left\lbrack {\left( \frac{b}{a} \right)^{2} - 1} \right\rbrack^{2}}{6 \cdot \eta \cdot \left( \frac{b}{a} \right)^{4}}}},{and}} & (18) \\{U_{rad} = {{\frac{1}{4} \cdot \frac{B_{r}}{\omega} \cdot V_{ab}^{2}} = {\frac{ɛ \cdot V_{0}^{2} \cdot \lambda \cdot \left( \frac{b}{\lambda} \right) \cdot \left( {\left( \frac{b}{a} \right)^{- 1} + 1} \right)}{2 \cdot \pi^{2}} \cdot {\left\lbrack {{E\left( \frac{2\sqrt{\frac{b}{a}}}{1 + \frac{b}{a}} \right)} - 1} \right\rbrack.}}}} & (19)\end{matrix}$The overall Q of the cavity 1512 including radiation can then beexpressed as:

$\begin{matrix}{Q = {\frac{\omega \cdot \left( {U + U_{rad}} \right)}{P_{ctr} + P_{out} + P_{b} + P_{\sigma_{e}} + P_{rad}} \cong {\frac{\omega \cdot (U)}{P_{ctr} + P_{out} + P_{b} + P_{\sigma_{e}} + P_{rad}}.}}} & (20)\end{matrix}$

If the energy stored in the radiation susceptance, U_(rad), is smallcompared to the energy stored in the interior of the cavity 1512, UP_(rad), are treated just like the previous losses. FIG. 16 illustratesa contour plot 1600 of the ratio of these stored energies, U_(rad)/U,with respect to the geometry terms b/a and b/λ. FIG. 16 illustrates thatthe stored energy in the external near field is small, compared to thestorage inside the cavity 1512, especially for a small b/A, which avoidshigher resonance modes.

A quality factor radiation component of, Q_(rad), can then be defined as

$\begin{matrix}{Q_{rad} = {\frac{\omega \cdot U}{P_{rad}} = \frac{3 \cdot \left( \frac{b}{a} \right)^{4} \cdot {\ln\left( \frac{b}{a} \right)}}{8 \cdot \pi^{3} \cdot \left( \frac{b}{\lambda} \right)^{4} \cdot {\left\lbrack {\left( \frac{b}{a} \right)^{2} - 1} \right\rbrack^{2}.}}}} & (21)\end{matrix}$To minimize the losses due to radiation, b/λ, should be made small andb/a kept close to unity; however, as is seen from a contour plot ofQ_(rad) in equation (21), b/λ is the dominant parameter. The total Q ofthe QWCCR 1500 can then be approximated by

$\begin{matrix}{Q \cong {\left( {\frac{8{\cdot \pi^{3} \cdot \left( \frac{b}{\lambda} \right)^{4} \cdot \left\lbrack {\left( \frac{b}{a} \right)^{2} - 1} \right\rbrack^{2}}}{3 \cdot \left( \frac{b}{a} \right)^{4} \cdot {\ln\left( \frac{b}{a} \right)}} + {\frac{R_{s}}{2 \cdot \pi \cdot \eta}\left\lbrack {\frac{\left( {\frac{b}{a} + 1} \right)}{\frac{b}{\lambda} \cdot {\ln\left( \frac{b}{a} \right)}} + 8} \right\rbrack} + {\tan\left( \delta_{e} \right)}} \right)^{- 1}.}} & (22)\end{matrix}$

The Q for each embodiment will depend on the ratio of the cavity 1512filling's intrinsic impedance to the surface resistance, R_(s)/η.Contour plots 1600 of the loaded quality factor, Q_(Γ=0), under perfectcoupling and the associated tip electric fields per square-root of powerare given for brass at 2.45 GHz below in the contour plot 1700 of FIG.17 and contour plot 1800 of FIG. 18. Note that Q_(Γ=0) is half the valuegiven by equation (22). As these figures show, maximum Q does notcoincide with maximum tip 1516 electric field, and in one embodiment theradius of the center conductor 1506 is small in order to achieve a highenough electric field for breakdown. Once breakdown does occur, theenergy stored in the cavity 1512 will be dumped into the plasma, and assuch, a larger Q would be desirable. Q also plays a role in the time ittakes a cavity 1512 to fill its energy store and for the electromagneticfields to build up.

Cavity Ringup and Energy Storage

The resonant QWCCR 1500 constitutes a second order system much like anRLC with a characteristic equation:

$\begin{matrix}{{{s^{2} + {\frac{R}{L}s} + \frac{1}{L \cdot C}} = {{s^{2} + {2 \cdot \zeta \cdot \omega_{n} \cdot s} + \omega_{n}^{2}} = {s^{2} + {\frac{\omega_{n}}{Q} \cdot s} + \omega_{n}^{2}}}},} & (23)\end{matrix}$with the natural resonance frequency ω_(n), the damping coefficient ofζ, and s, the usual frequency domain variable. This highlights thedirect relationship between Q and the damping coefficient as Q⁻¹=2ζ. Itis well known that the time domain response of a second order system hasa transient portion that decays exponentially with a time constant(ζω)⁻¹ or 2Q/ω. After 5 time constants, these transients are generallyconsidered to have died out, the cavity 1512 will be filled with energyand the fields will have reached a steady state value. The energy storedin the cavity 1512 is determined by solving equation (5) for U=P_(L)Q/ω. Further equations would include coupling coefficients and timesdependences.

A QWCCR 1500 at 2.45 GHz with Q of 100 would take 65 ns to ring up, fastenough even for proper ignition timing of higher speed engines. Theenergy accumulated would only be 6.5 μJ per 1 kW input power. If 0.2 mJis assumed as a minimum for ignition, and with typical ignition energiesmuch higher than that, energy stored in the cavity 1512 will only be aminor contributor toward ignition. The bulk of the ignition energy willcome from the power fed to the cavity 1512 after breakdown.

Analysis Results

The preceding approximate analysis reveals the following factors toconsider when designing the geometry of a QWCCR 1500 with a large tip1516 electric field. The parameter of highest significance is a smallcenter conductor 1506 radius, a, possibly sharpened, as E_(a) isdirectly inversely proportional to a. It is desirable to maximize theterm η Q P_(L), on which E_(a) depends in the square root. This requireskeeping the intrinsic impedance, η, of any filler material high, feedingthe QWCCR 1500 resonator as much power, P_(L), as possible andmaximizing Q. The latter is accomplished by increasing the volume energystorage U of the cavity, and minimizing surface and radiation losses.Radiation losses are excessive for large b/λ and the ratio b/(λ/a) isalmost on equal footing with the center conductor 1506 radius inincreasing tip electric field. As b/λ shrinks, conductor surface 1502,1504, 1506 plus dielectric losses are on equal footing with radiationlosses. In this region, the particulars of the materials and thefrequency need to be examined. In various embodiments, designs areaccomplished by examining contour plot 1700 of FIG. 17 and contour plot1700 of FIG. 18, and using these contour plots 1700, 1800 as designtools to approximate the values realized in practice.

Quarter Wave Coaxial Cavity Resonator Design and Implementation

In one embodiment, the QWCCR 1500 is created out of alloy 360 brass. Anair dielectric is used and a design field strength requirement ofgreater than 30 kV cm⁻¹ is selected. Such field strength is sufficientto cause breakdown under atmospheric conditions. Using FIG. 19 andselecting a 100 W power input, the region of the contour plot 1900indicating field strength greater than 3 kV cm⁻¹ W⁻1/2 is identified.The QWCCR 1500 has a major diameter of ¼″ or b/λ=0.026 and a minordiameter of 1/32″ or b/a ratio of 8, corresponding to an estimated fieldstrength of 3.5 kV cm⁻¹ W⁻1/2 and a Q_(Γ)=0 of 270.

FIG. 20 shows this embodiment of an exemplary QWCCR spark plug 2000 witha 14-1.25 mm spark plug thread 2002. The coaxial cable 2004 enters thebase 2008 of the cavity 1512. The coupling is accomplished through asmall loop 2006, created by the coaxial cable 2004 center conductorattaching back to the shield of the coaxial cable 2004. Proper impedancematching between the cavity 1512 and the coaxial cable 2004 isaccomplished by rotating the coaxial cable 2004 thereby turning theplane of the small loop 2006. This adjusts the magnetic linkage betweenthe fields in the base of the cavity 1512. Once a coupling close to 1:1is achieved, for example by measuring with an HP8753D network analyzer,the coaxial cable 2004 is crimped and soldered in place. The achievedcoupling and the loaded quality factor Q_(Γ)=0 is measured to be 258 ata resonant frequency of 2430.73 MHz. Note that the quality factor wassomewhat lower than predicted by analysis.

Theoretical surface resistance is generally not achievable due tosurface imperfections and contaminations, such as oxidation. Themagnetic fields in the base 2008 of the cavity 1512 are slightlydisturbed by the presence of the coupling structure, which increases thelosses slightly. Soldering also created a small amount of lowerconductivity surface around the base of the center conductor 1506. Witha rounded tip 1516, the measured Q_(Γ)=0 of 253 is suitable forproducing a field strength of 3.46 kV cm-1 W-½, or 34.6 kV cm-1 at 100W. To operate at the estimated 300 kV cm-1 necessary under an engine's10:1 compression ratio, in one embodiment the product η Q PL isincreased by 100 according to equation (10). In another embodiment, thetip 1516 radius is reduced to 1/10 the initial diameter to intensify thefield. In another embodiment, a gas temperature increase lowers thisrequirement per equation (2). In another embodiment, roughness surfaceimperfections on the tip 1516 of the center conductor 1506 will lowerthe threshold by concentrating the field.

Design Refinement

In various embodiments, the QWCCR 1500 is optimized by changes to thegeometry to reduce radiation losses through the aperture, and bymaintaining a high volume to interior surface area ratio. The disclosedtheoretical analysis allows the prediction of cylindrical designperformance using the derived equations and design graphs. Inembodiments, the radius of the center conductor 1506 at the tip 1516 ischosen to cause breakdown at a given desired field strength, much likechoosing appropriate gap spacing for a spark plug 106. In spark plugs106 this allows energy to build up prior to the breakdown event;similarly the QWCCR 1500 with a larger exposed tip area creates plasmaat breakdown, aiding in the ignition of the mixture. In embodiments,improvements in the QWCCR 1500 design are made through selection of lowloss materials to improve the quality factor and the associated resonantfield step-up to higher potentials.

Reduced Aperture Geometries

In embodiments, the QWCCR 1500 has a reduced aperture geometry, bynarrowing the cavity 1512 near the opening 1514, or aperture. Pointeddischarge tips 1516 at the end of the center conductor 1506 intensifyand concentrate the electric fields. FIGS. 21a, 21b, 21c, and 21dillustrate several possible embodiments for a narrow aperture QWCCR2100, 2102, 2104, 2106. The embodiment of FIG. 21a illustrates a QWCCRhaving a rectangular cavity with a stepped aperture 2100. The embodimentof FIG. 21b illustrates a QWCCR having an oval cavity with a narrowaperture 2102. The embodiment of FIG. 21c illustrates a QWCCR having arectangular cavity with a curved aperture 2104. The embodiment of FIG.21d illustrates a QWCCR having a tapered cavity with a narrow aperture2106. These exemplary embodiments illustrate sample geometries of narrowaperture QWCCRs 2100, 2102, 2104, 2106. Various other configurations andgeometries are possible as would be understood by one familiar in theart. Although the geometries of the above embodiments cause the resonantfields to be slightly distorted when compared to a cylindrical QWCCR1500, the different geometries do not significantly affect the functionof the narrow aperture QWCCRs 2100, 2102, 2104, 2106. However, oneparticular result of the closer proximity of the center and outerconductors at the opening 1514, or aperture, is an additional reactiveor capacitive loading. The additional reactive loading tends to decreaseresonance frequency slightly, and also makes the effective length of thenarrow aperture QWCCRs 2100, 2102, 2104, 2106 slightly shorter. Suchreactive loading can be enhanced by other known methods that produce RFcapacitance, for example by using enlarged metal tips 1516 havinggeometries such a spheroid-like shapes or teardrop-like shapes, or byplacing dielectric materials around the tip. However, the effectivelength is not significantly shortened and the use of different shapedtips or dielectrics may not be practical for all applications.

Tapered Geometries

Referring now to FIGS. 22a and 22b , a threaded tapered QWCCR 2200 isillustrated. In FIG. 22a , the threaded tapered QWCCR 2200 isillustrated in two dimensions. In FIG. 22b , the threaded tapered QWCCR2200 is illustrated in three dimensions. The threaded tapered QWCCR 2200comprises a cavity 1512 that is tapered and a center conductor 1506 witha tip 1516 that extends through an opening 1514 in a front threadedconnector 2202. The threads of the front threaded connector 2202facilitate mounting the threaded tapered QWCCR 2200 to a combustionengine. A rear threaded connector 2204 accepts a threaded electricalconnector (not shown) from an ignition control system; the threadedelectrical connector mates with an electrical connector 2206 and passesthe RF energy through dielectric seals 2208, shown as crosshatchedregions in FIG. 22a , to dual on-axis inductive coupling loops 2212. Thedual on-axis inductive coupling loops 2212 inductively couple the RFenergy to the center conductor 1506. Internal threaded portions 2210facilitate assembly of the QWCCR 2200. In an embodiment, the rearthreaded connector 2204 and electrical connector 2206 accept a 50 Ohmcoaxial connector.

The dielectric seals 2208 are placed towards the rear, or base 2214, ofthe threaded tapered QWCCR 2200 to prevent losses to the electric fieldnear the center conductor 1506 and tip 1516. Tapering the cavity 1512and narrowing the opening 1514, or aperture, increase the electric fieldat the tip 1516 by squeezing the electric field into a smaller radialextent. Maintaining a larger diameter in the cavity 1512 near the base2214 of the threaded tapered QWCCR 2200 helps to reduce conductionlosses, thereby allowing a high Q, as it allows the resonant magneticfield to spread-out and have a lower valued tangential component at thesurface of the conductors such as the base 2214 and center conductor1506. The threaded tapered QWCCR 2200 advantageously reduces apertureradiation losses by keeping the aperture size, or opening 1514, smallrelative to the operating wavelength, λ, or stated another way, bykeeping the size of the aperture, or opening 1514, small in relation tothe length of the cavity 1512. The length of the cavity 1512 isadvantageously chosen as λ/4 although larger odd multiples of λ/4 couldalso be used. However, if the length of the cavity 1512 is longer thanλ/4 then undesirable conduction losses may occur, depending on thegeometry of the cavity 1512, for example through the greater surfacearea of the cavity wall due to the surface resistance, R_(S). Althoughlarger cavity 1512 may increase Q, greater surface areas may lower Q,especially for surfaces areas where the magnetic field strength ishighest. Therefore, to reduce conduction losses, the threaded taperedQWCCR 2200 utilizes a λ/4 cavity 1512.

In an embodiment, the threaded tapered QWCCR 2200 is designed to replacean existing spark plug 106. Using a λ/4 cavity 1512 that is comparableto the length of a spark plug, for example 3 cm, results in an operatingfrequency, λ, of approximately 2.45 Ghz. However, there aredisadvantages to using this high of an operating frequency, λ. Highfrequency generators can sometimes be more expensive than lowerfrequency generators, depending on the operating frequency, λ. Also,conduction losses in the cavity 1512 increase with operating frequency,λ. Therefore, using lower frequencies would advantageously increase theQ of the threaded tapered QWCCR 2200, and QWCCRs 1550 in general.

Several methods can be utilized to reduce the operating frequency, λ,without increasing the overall length of the cavity 1512. In anembodiment, the cavity 1512 can be filled with a dielectric. Howeverfilling the cavity 1512 with a dielectric has the disadvantage that thedielectric increases energy loss. In another embodiment, the cavity 1512can utilize a folded geometry to increase the effective length of thecavity 1512 without increasing the overall length of the QWCCR 1550. Inanother embodiment, the QWCCR 1550 utilizes reactive loading of thecavity 1512. The folded cavity geometry and reactive loading methods aredescribed below.

Folded Cavity Geometries

Referring now to FIGS. 23a and 23b , a threaded folded cavity QWCCR 2300is illustrated. In FIG. 23a , the threaded folded cavity QWCCR 2300 isillustrated in two dimensions. In FIG. 23b , the threaded folded cavityQWCCR 2300 is illustrated in three dimensions. The threaded foldedcavity QWCCR 2200 comprises a folded cavity 2302 that reduces the sizeof the resonator by folding, or nesting, concentric portions of thecavity 2302 on itself. The folded cavity 2302 achieves substantialreductions in the length of the threaded folded cavity QWCCR 2200 whilemaintaining the same resonant frequency of a longer QWCCR 1500. Thefolding, or nesting, of the folded cavity 2302 advantageously allows thethreaded folded cavity QWCCR 2300 to have both a large diameter base2214 and a small diameter aperture, or opening 1514. The large diameterof the base 2214 in the high magnetic field region reduces conductionlosses, while the smaller diameter of the aperture, or opening 1514,concentrates the electrical field and reduces losses relating toaperture radiation.

To explain the function of the folded cavity 2302 of the threaded foldedcavity QWCCR 2300, a resonant standing quarter wave can be thought of astwo interfering waves bouncing back and forth between the electricallyshorted base 2214 and the electrically open aperture, or opening 1514,of the folded cavity 2302. The path is illustrated in one directionusing arrows in FIG. 23a . The folded cavity 2302 comprises an innerconcentric hollow conductor 2316 and an outer concentric hollowconductor 2314. The inner concentric hollow conductor 2316 and the outerconcentric hollow conductor 2314 serve dual roles as both inner andouter conductors of the resonator. The walls of sections of the foldedcavity 2302 comprise the surfaces, 2304, 2306, of the inner concentrichollow conductor 2316, and the surfaces, 2308, 2310 of the outerconcentric hollow conductor 2314.

The folded cavity 2302 reduces the physical length of the threadedfolded cavity QWCCR 2300 to approximately one third of the size of anunfolded QWCCR 1500. Effectively, the folded cavity 2302 of the threadedfolded cavity QWCCR 2300 behaves similarly to three joined pieces ofcoaxial transmission line with differing dimensions. This is illustratedin FIG. 23c , which shows the rough equivalent of the threaded foldedcavity QWCCR 2300 if it were unfolded. The unfolded geometry has anend-to-end length that is close to multiple of a quarter wavelength, butnot exactly realizable physically due to how the inner concentric hollowconductor 2316 and an outer concentric hollow conductor 2314 areconnected. The dotted line illustrates the wave reflection point in thefolded cavity 2302. In embodiments, additional concentric hollowconductors are utilized. In embodiments, the geometries of one or moreof the concentric hollow conductors is altered from cylindrical toanother geometry, for example a tapered geometry. In embodiments, thereare an odd number of oppositely directed concentric hollow conductors inorder to have the opening 1514 opposite the rear threaded connector 2204and electrical connector 2206.

In an embodiment, the dimensions of the inner concentric hollowconductor 2316 and an outer concentric hollow conductor 2314 areselected to result in the same coaxial transmission line impedances toavoid impedance discontinuities other than the base 2214 and aperture,or opening 1514. Referring back to Equations (6) and (7), at resonance,the stored magnetic and electric time average energies are equal. Theenergy store per unit length is not directly dependent on the actualradii of the inner concentric hollow conductor 2316 and an outerconcentric hollow conductor 2314, but instead are a function of theircharacteristic impedance, i.e., the radius ratio. Therefore the foldedcavity 2302 will behave similarly to a longer unfolded cavity 1512 ifthe characteristic impedance of each section is maintained.

However, small washer shaped regions of potential impedancediscontinuities exist at the transition points between the innerconcentric hollow conductor 2316, the outer concentric hollow conductor2314, and the wall 2320. In an embodiment, to eliminate or reduce theimpedance discontinuities at the transition points, small washer shapeddielectric seals 2312 are placed at the transition points. In anembodiment, to eliminate or reduce the impedance discontinuities at thetransition points, the radius or geometries of the center conductor aremodified. Because the center conductor is a folded cavity 2302, thecenter conductor includes the surface 2304 of the outer concentrichollow conductor 2314, and the surface 2308 of the inner concentrichollow conductor 2316. Therefore the surfaces 2304, 2308 and concentrichollow conductors 2314, 2316 are altered slightly so that the transitionpoints have the same characteristic impedances as the rest of the foldedcavity 2302.

The transition regions may be short enough that corrective small washershaped dielectric seals 2312 may not be necessary. The transitionregions can be viewed as lumped reactive loads on the line. In anembodiment, small washer shaped dielectric seals 2312 are placed in thetransition regions or other areas of the folded cavity 2302. Thedielectric seals 2312 also function as seals for the folded cavity 2302to prevent materials from the combustion chamber, or other contaminants,from entering the folded cavity 2302. Because the threaded folded cavityQWCCR 2300 will become hot from contact with the combustion chamber andhot gases, the small washer shaped dielectric seals 2312 are kept shortto prevent any difference in their thermal expansion rate from creatingphysical stresses on the inner concentric hollow conductor 2316 or theouter concentric hollow conductor 2314. The small washer shapeddielectric seals 2312 are also kept short to prevent losses in thedielectric material. Note that in some placements of a dielectric seals2312, such as when sandwiched between cavity members 2314, 2316, 2320, astanding RF wave will pass through the same dielectric seal 2312 twice,once when the standing wave is travelling in a first direction, and thenagain as it is reflected in the other direction. In such situations, thedielectric seal 2312 will have the same effect as a dielectric seal 2312that is twice as thick.

Whereas a single unfolded cavity generally uses the same material alongthe entire length of the cavity 1512, the folded cavity 2302 can utilizedifferent materials for the wall 2320, the inner concentric hollowconductor 2316, and the outer concentric hollow conductor 2314,collective the cavity members 2314, 2316, 2320. In embodiments, one ormore conductor materials are used for the wall 2320, the innerconcentric hollow conductor 2316, and the outer concentric hollowconductor 2314. In embodiments, the surfaces 2304, 2306, 2308, 2310,2318 comprise different materials. For example, where high conductivityis important, for example the high magnetic field regions of the base2214, copper can be selected as the material. In high temperatureregions, such as the tip 1516, more resilient conductive material can beselected. Selection of different materials advantageously allows thedesigner to use expensive materials sparingly.

The threaded folded cavity QWCCR 2300 also has a center conductor 1506with a tip 1516 that extends through an opening 1514 in a front threadedconnector 2202. The threads of the front threaded connector 2202facilitate mounting the threaded folded cavity QWCCR 2300 to acombustion engine. A rear threaded connector 2204 accepts a threadedelectrical connector (not shown) from an ignition control system; thethreaded electrical connector mates with an electrical connector 2206.

Analysis of Power Losses in Folded Cavity Geometries

The energy store per unit length is a function of the cavity member's2314, 2316, 2320 characteristic impedance, however the nesting of thecavity members 2314, 2316, 2320 create sections of different sizesrather than a more uniform cavity 1512. The losses in the folded cavity2302 will therefore be somewhat different than a more uniform cavity1512. Assuming that field fringing at the transition regions isnegligible, and that the fields of the resonance are approximatelytransverse electromagnetic mode (TEM) standing quarter wave sinusoids sothat equations (3) and (4) describe the waves, β=2/λ, and I₀ is someassumed amplitude. For a cylindrical conductor surface, with surfaceresistance R_(s), and radius r_(o), the time average power dissipated isgiven by the surface integral in equation (11) and equation (2) can berecast in terms of electrical angles so that β·dz=dθ_(z):

$\begin{matrix}{\begin{matrix}{P_{cyl} = {\frac{R_{s}}{2}{\int_{A}{{H_{//}}^{2} \cdot {dA}}}}} \\{P_{cyl} = {\frac{I_{o}^{2} \cdot R_{s}}{4 \cdot \pi \cdot \beta \cdot r_{o}} \cdot {\int_{\theta_{z\; 1}}^{\theta_{z\; 2}}{{{\cos^{2}\left( \theta_{z} \right)} \cdot d}\;\theta_{z}\quad}}}}\end{matrix}\quad} & (24)\end{matrix}$

Considering an area interpretation of the integral over cos²θ, it can beseen that losses per unit length decrease as the open end of the cavityis approached. This suggests that using large radii toward the shortcircuited end of the resonant line is more important in reducing lossesthan using them toward the open circuited end. If constant powerdissipation per unit length is desired, the radii could vary as r₀·cos²θresulting in a tapered shape. The sidewall surface loss of (10) wouldthen reduce to

$\begin{matrix}{P_{\cos^{2}} = {{\frac{I_{o}^{2} \cdot R_{s}}{4 \cdot \pi \cdot \beta \cdot r_{o}} \cdot \Delta}\;\theta_{z}}} & (25)\end{matrix}$

Through a similar area integration the ohmic power losses for a circularannulus with inner and outer radius a′ and b respectively, at a distancez along the line is determined as:

$\begin{matrix}{P_{anu} = {\frac{I_{o}^{2} \cdot R_{s}}{4 \cdot \pi} \cdot {\ln\left( \frac{b}{a^{\prime}} \right)} \cdot {\cos^{2}\left( \theta_{z} \right)}}} & (26)\end{matrix}$Placing annuli close to the short circuited end of the transmissionline, where the magnetic fields are higher, will result in largerlosses. The power dissipated by the standing wave in a low lossdielectric filling, with effective conductivity, σ_(e)=ω·∈·tan δ, in thecoaxial line with inner radius, a, and outer radius, b, extendingbetween distances z₁ and z₂ along the line is

$\begin{matrix}{\begin{matrix}{P_{\sigma_{e}} = {\frac{\sigma_{e}}{2}{\int_{Vol}{{E}^{2} \cdot {dv}}}}} \\{P_{\sigma_{e}} = {\frac{1}{2} \cdot I_{o}^{2} \cdot Z_{o} \cdot {\tan(\delta)} \cdot {\int_{\theta_{z\; 1}}^{\theta_{z\; 2}}{{{\sin^{2}\left( \theta_{z} \right)} \cdot d}\;\theta_{z}}}}}\end{matrix}\quad} & (27)\end{matrix}$for the sinusoidal resonant field distribution. Considering the integralover sin²θ in equation (27), the closer a dielectric filling is placedto the open end of the resonator, the higher the losses will be. Thequality factors, Q, of the resonator can now be estimated as

$\begin{matrix}{Q = \left( {\sum\limits_{i}\frac{P_{i}}{\omega \cdot U}} \right)^{- 1}} & (28)\end{matrix}$

Prior to analyzing any design, the section lengths of the resonator haveto be converted to electrical degrees so the integrals can be evaluated.The dielectric constant of the transition regions will affect theangular electrical line length. The relative dielectric constantrequired to maintain the same line impedance when the conductor radiusratio changes from b₀/a₀ to b₁/a₁ is given by:

$\begin{matrix}{ɛ_{r} = \left\lbrack \frac{\ln\left( {b_{1}/a_{1}} \right)}{\ln\left( {b_{0}/a_{0}} \right)} \right\rbrack^{2}} & (29)\end{matrix}$

Despite having the largest radii, the wall 2120 contributes the greatestlosses because it experiences the strongest magnetic fields. Thereforekeeping the cavity members 2314, 2316, 2320 short will help the Q orquality of the threaded folded cavity QWCCR 2300. Further, improvementsto the threaded folded cavity QWCCR 2300 can be made by increase theradii. However, the radii cannot be increased beyond the point wherehigher order harmonics, or modes, start to appear in the threaded foldedcavity QWCCR 2300. This suggests an upper limit of 2π(b+a)<λ/2 for theradii. This suggests that a high Q folded QWCCR can be created byincreasing the radii.

High Q Folded QWCCR

Referring now to FIGS. 24a and 24b , a high Q folded QWCCR 2400, and ahigh Q folded tapered QWCCR 2410 are presented. The quality factor, orQ, of a folded cavity 2302 is increased by choosing larger radii for thewall 2320, the inner concentric hollow conductor 2316, and the outerconcentric hollow conductor 2314. Although the radii is increased forthe folded cavity 2302, the opening 1514 or aperture remains narrow dueto the folded design, thus preventing significant radiative lossesthrough the opening 1514. In embodiments, a dielectric plug 2402, ordielectric seal, prevents material from the combustion chamber fromentering the folded cavity 2302. In FIG. 24b , the high Q folded taperedQWCCR 2410 additionally has a tapered discharge electrode 2412 and atapered opening 2414.

QWCCR with Helical Reactive Loading

Referring now to FIGS. 24a and 24b , a high Q folded QWCCR 2400, and ahigh Q folded tapered QWCCR 2410 are presented. The quality factor, orQ, of a folded cavity 2302 is increased by choosing larger radii for thewall 2320, the inner concentric hollow conductor 2316, and the outerconcentric hollow conductor 2314. Although the radii is increased forthe folded cavity 2302, the opening 1514 or aperture remains narrow dueto the folded design, thus preventing significant radiative lossesthrough the opening 1514. In embodiments, a dielectric plug 2402, ordielectric seal, prevents material from the combustion chamber fromentering the folded cavity 2302. In FIG. 24b , the high Q folded taperedQWCCR 2410 additionally has a tapered discharge electrode 2412 and atapered opening 2414.

Experimental Testing

For an initial test case, the structure shown in FIG. 23c was assembledout of commercially available brass tubing sizes targeting a resonancefrequency of 433 MHz (69.3 cm wavelength) with dimensions c1, c2, c3,c4, and c5 as given in Table I and Table II:

TABLE I Dimension and properties of coaxial line sections Coax c1 c2 c3c4 c5 b [cm] 1.19 1.19 0.57 0.57 0.24 a [cm] 0.64 0.30 0.30 0.13 0.13ε_(r) 1 1 1 5.8 1 tan(δ) 0 0 0 .005 0 Z_(o) [Ω] 38 82 38 38 37 Δz [cm]4.90 1.11 3.53 0.53 6.51 Δθ_(z) [°] 25.5 5.8 18.3 6.7 33.8 Q_(i) 17005400 1900 1900 2200 Δz Q_(i) [cm⁻¹] 8400 5800 6600 1000 14500

TABLE II Dimensions and location of annuli Annulus a0 a1 a2 b [cm] 1.191.19 0.57 a′ [cm] 0.64 0.30 0.13 z [cm] 0.00 5.46 9.80 θ_(z) [°] 0 28.453.0 Q_(i) 30300 18000 34700

The value 0.0104Ω was used as the surface resistance, R_(S), of brass at433 MHz. Note that the impedance matching dielectric at the firstjunction, which should have had a relative dielectric constant of 4.7,was omitted. Provided the length of the mismatch is short with respectto wavelength, no serious reflections will occur, and instead thejunction steps will appear as small shunt capacitances. The magnitude ofthese capacitances is on the order of 0.2 pF which is located in aregion of relatively low electric field magnitudes. For the purpose ofthis analysis, this shunt capacitance will be ignored. The calculatedcombined unloaded quality factor is 414. This is about 2.5 times greaterthan if the resonator had been made out of the smallest diametersection, c5, for the entire length but naturally lower than if thelarger diameters of section, c1, had been used throughout. It isapparent from the calculated Q_(i), that the annuli losses areinsignificant. However, the dielectric losses should not be discounted,despite the fact that the dielectric is set back from the maximumelectric fields by 33.8°. Also of note is the fact that despite havingthe largest radii, the cylinders of the c1 section contribute thelargest losses as it experiences the strongest magnetic fields. As afigure of merit, that can be used to compare the transmission linesections, Δz Q_(i) was also computed. This metric highlights thedielectric losses.

A compact cavity with larger radii, comparable to FIG. 24a , but withoutthe pointed tip 1506, was designed with dimensions given in Table IIIand Table IV:

TABLE III Dimension and properties of coaxial line sections Coax c1 c2c3 c4 c5 c6 c7 b[cm] 2.53 2.53 1.19 1.19 0.56 0.56 0.28 a[cm] 1.27 0.600.60 0.28 0.28 0.16 0.16 ε_(r) 1 1 1 1 1 5.8 1 tan(δ) 0 0 0 0 0 .005 0Z_(o)[Ω] 42 88 41 87 42 31 34 Δz[cm] 4.08 2.54 2.46 1.02 3.41 0.32 3.07Δθ_(z) [°] 21.2 13.2 12.8 5.3 17.7 4.0 15.9 Q_(i) 5000 5600 6500 383005400 3800 30200 Δz Q_(i) 20600 14200 16000 38900 18300 1300 92700 [cm⁻¹]

TABLE IV Dimensions and location of annuli Annulus a0 a1 a2 b [cm] 2.532.53 1.19 a′ [cm] 1.27 0.60 0.28 z [cm] 0.00 5.35 9.58 θ_(z) [°] 0 27.849.8 Q_(i) 33600 20500 12300

The calculated, combined unloaded quality factor for this second designis 834, twice the small radii design quality factor. Note that anadditional reduction in radii in going from c5 to c7 (the dielectricplug seal 2402 being c6; the center conductor 1506 being c7) wasincluded without a reversal in direction and without accounting for theannuli losses in the reduction as the losses on the annuli are very low,i.e. their Qs are very high.

As a comparison and using the same TEM assumptions, the quality factorof a cos² (θ) tapered, unfolded cavity of quarter wavelength using airas a dielectric was derived using:

$\begin{matrix}{E_{a} = {\frac{\eta}{a_{tip}}\sqrt{\frac{2 \cdot Q \cdot P}{\pi^{3} \cdot Z_{o}}}}} & (30) \\{U = \frac{I_{o}^{2} \cdot Z_{o}}{16 \cdot f}} & (31)\end{matrix}$for the energy stored, equation (25) for the tapered side conductors andequation (26) for the base conductor annulus at the shorting end. Theresult without accounting for the dielectric is given by:

$\begin{matrix}{Q_{\cos^{2}} = \left\lbrack {{\frac{\lambda \cdot R_{s}}{2 \cdot \pi^{2} \cdot Z_{o}} \cdot \left( {\frac{1}{a} + \frac{1}{b}} \right)} + \frac{4 \cdot R_{s}}{\pi \cdot \eta}} \right\rbrack^{- 1}} & (32)\end{matrix}$The dielectric losses increase dramatically toward the open-circuitedend of the cavity in such a tapered design since the sin² (θ) term underthe integral in equation (27) is turned into a tan² (θ) term by thetapering:

$\begin{matrix}{\begin{matrix}{P_{\sigma_{e}} = {\frac{{\omega \cdot ɛ}{\cdot \eta^{2} \cdot I_{o}^{2}}}{4 \cdot \pi} \cdot {\int_{z\; 1}^{z\; 2}{\int_{a}^{b}{\frac{\sin^{2}\left( {\beta \cdot z} \right)}{r \cdot {\cos^{2}\left( {\beta \cdot z} \right)}} \cdot {dr} \cdot {dz}}}}}} \\{P_{\sigma_{e}} = {\frac{1}{2} \cdot I_{o}^{2} \cdot Z_{o} \cdot {\tan(\delta)} \cdot {\int_{\theta_{z\; 1}}^{\theta_{z\; 2}}{{{\tan^{2}\left( \theta_{z} \right)} \cdot d}\;\theta_{z}}}}}\end{matrix}\quad} & (33)\end{matrix}$

In an actual implementation, the length would be slightly shorter thanλ/4, to allow an aperture that would have capacitance. Nevertheless,filling the entire cavity would create excessive losses. Since theprevious two example cavities were mostly hollow, the tapered cavitywill be assumed to be made of brass with an air dielectric throughout.The resulting quality factors of the tapered design using the same radiiat the shorted base as the two sectioned cavities are: 418 for theinitial and 927 for the enlarged radii respectively. These values arequite similar to the values calculated for the discretely sectioneddesigns; depending on how well the step tapered sections fit the cos²(θ) distribution, a first cut estimate of a sectioned design could beobtained using the tapered results. One could also construct such atapered cavity by approximate the cos²(θ) taper with a straight line,thereby making a conical similar to FIG. 22 a.

Measurement of the quality factor and the degree of coupling on aHP8753D network analyzer resulted in an unloaded Q of 340 at a resonancefrequency of 425.75 MHz for the small radii geometry. The larger radiigeometry resulted in an unloaded Q of 760 with a resonance frequency of439.87 MHz. A conical brass resonator was constructed having a baseradius of 1.5″ and a b/a ratio of 6 for an approximate line impedance of108Ω. The resonance frequency of the conical brass resonator had beenmeasured at 960 MHz with an unloaded Q of 1800. Calculations using thecos² (θ) taper results would predict a quality factor of 2100, with a17% difference from the conical measured result. For the folded cavitiesconstructed, the frequencies of the implementations of the first andsecond cavity differ from the design frequencies by 1.7% and 1.6%respectively. As is generally the case, the measured quality factorswere both lower than the theoretically calculated values. The respectivedifferences for the small and large radii cavities were 18% and 9%. Notethat disturbance of the electromagnetic fields at the base of the cavitydue to the coupling structure have been ignored in the analysis. Thereis also potential for error due to conductivity differences, surfaceimperfections, solder joints and uncertainty in the dielectricparameters.

CONCLUSION

The numerous embodiments described above are applicable to a number ofdifferent applications. The embodiments of the QWCCR produce large andcontrollable sustained average power levels compared to conventionalspark plug systems. Sustained high power levels are beneficial forignition of ultra lean mixtures leading to higher combustionefficiencies and the associated fuel-savings. The QWCCR achieves astep-up of the energy to a potential necessary for breakdown without theinefficiencies of a conventional ignition coil. QWCCR embodimentsutilizing reduced aperture geometries reduce radiative losses withoutsignificantly reducing resonant characteristics thereby increasing theQ, or quality, of the QWCCR. QWCCR embodiments utilizing reactive loadsand folded cavity geometries permit the use of lower operatingfrequencies and increase the Q of the QWCCR, thereby permitting the useof less expensive power supplies and increasing the amount of power thatis transferred into the corona discharge plasma. Operation of the QWCCRwith high power corona discharge plasma is beneficial for demandingcombustion applications. Using corona discharge plasma as an ignitionsource in lieu of more traditional spark plug technologies has manyadditional applications apparent to one of ordinary skill in the art.

The embodiments of the invention shown in the drawings and describedabove are exemplary of numerous embodiments that may be made within thescope of the appended claims. It is contemplated that numerous otherconfigurations of the disclosed system, process, and device for ignitingcombustible materials in combustion chambers may be created takingadvantage of the disclosed approach. It is the applicant's intentionthat the scope of the patent issuing herefrom will be limited only bythe scope of the appended claims.

What is claimed is:
 1. A quarter wave coaxial cavity resonator,comprising: a plurality of concentric nested cavity members arranged toform a folded cavity, the plurality of concentric nested cavity membersincluding an outer concentric hollow conductor and an inner concentrichollow conductor defining an aperture; a reactive load center conductorincluding a tip, at least a portion of the reactive load centerconductor disposed in the folded cavity, wherein the folded cavity iscoupled to a radio frequency power source to produce a sustained RFoscillation of an operating wavelength in the quarter wave coaxialcavity resonator, wherein the operating wavelength is derived from anoperating frequency in a range between 750 MHz to 7.5 GHz, wherein an RFcorona is formed at the tip of the reactive load center conductor whenthe sustained RF oscillation of the operating wavelength is produced inthe quarter wave coaxial cavity resonator, and wherein a length of thefolded cavity is no longer than approximately one fourth of theoperating wavelength.
 2. The quarter wave coaxial cavity resonator ofclaim 1, wherein the reactive load center conductor is a corrugatedreactive load element.
 3. The quarter wave coaxial cavity resonator ofclaim 1, wherein the reactive load center conductor is a dielectriccoated center conductor.
 4. The quarter wave coaxial cavity resonator ofclaim 1, further comprising a threaded body surrounding the aperture andadapted to fit a spark plug socket.
 5. The quarter wave coaxial cavityresonator of claim 1, further comprising a dielectric seal positionedabout the reactive load center conductor.
 6. The quarter wave coaxialcavity resonator of claim 1, wherein the tip is generally cylindrical.7. The quarter wave coaxial cavity resonator of claim 1, wherein the tipis generally spherical.
 8. The quarter wave coaxial cavity resonator ofclaim 1, wherein the tip is curved.
 9. The quarter wave coaxial cavityresonator of claim 1, wherein the tip includes a point.
 10. The quarterwave coaxial cavity resonator of claim 1, wherein the tip is generallyteardrop shaped.
 11. The quarter wave coaxial cavity resonator of claim1, further comprising a loop coupling to couple an energy shapingcircuit to the reactive load center conductor of the quarter wavecoaxial cavity resonator.
 12. The quarter wave coaxial cavity resonatorof claim 1, wherein the tip of the reactive load center conductorextends through the aperture.